Chaotic nature of holographic QCD

Dmitry S Ageev

doi:10.1103/physrevd.104.126013

Dmitry S Ageev

Open Access

https://doi.org/10.1103/physrevd.104.126013

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Abstract

In this paper, we bring together two topics in the holographic correspondence---quantum chaos and quark-gluon plasma (QGP). We establish that the first relativistic correction to drag force experienced by a charge carrier moving through a thermal medium (for example, a quark in QGP) at a constant velocity is fixed by the butterfly velocity. Moreover, we show that this result is robust against stringy corrections and anisotropy. For the jet quenching parameter, we find that it is related to the butterfly velocity along the momentum broadening direction and temperature. This opens a way to the reconstruction of butterfly velocity of quark-gluon plasma and other strongly coupled systems experimentally from rather simple observables.

Highlights

Many properties of strongly interacting quantum systems are known to carry large imprint of universality
In this paper we argue that the drag force and jet quenching parameter has the imprint of universality analogous to (1)–(3)
To reveal some nontrivial relation between qand chaotic characteristics, we focus on the jet quenching for some

Summary

INTRODUCTION

Many properties of strongly interacting quantum systems are known to carry large imprint of universality. We focus mainly on the drag force [9,10] and jet quenching parameter [11] Both are related to the energy and momentum loss for projectiles moving in a strongly interacting quantum system (quark-gluon plasma). In this paper we argue that the drag force and jet quenching parameter has the imprint of universality analogous to (1)–(3) We show how they are related to the butterfly velocity and temperature. We obtain that in the holographic systems for small velocities v of charge carrier (quark), the properly normalized momentum loss dpσ=dt is fixed by the butterfly velocity up to a first “relativistic,” i.e., v3 term dpσ=dt 1⁄4 −v − B · v3 þ Á Á Á ; B ðd 1 − 1Þv2B ð5Þ where we denote the normalization factor by σ One may consider this identity as the microscopic manifestation of the relations between diffusion and butterfly velocity. In the Supplemental Material [19] we provide all necessary details of calculations

THE CHAOTIC ORIGIN OF THE DRAG FORCE

JET QUENCHING AND BUTTERFLY VELOCITY

RELATION BETWEEN BUTTERFLY VELOCITY AND JET QUENCHING VIA DRAG FORCE

DISCUSSION